Uncertainty Quantification

Uncertainty quantification

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The design of efficient electrotechnical devices requires deep insight into the device’s electromagnetic field distribution. Today, this is typically obtained by computer simulations instead of physical prototypes. On the other hand, the available input data, e.g. boundary conditions, geometry, material curves, include uncertainties, e.g. unknown errors due to measurements or lack of knowledge. The influence of these errors can be characterized by uncertainty quantification. In the mathematical models, the corresponding parameters are substituted by random variables to describe the uncertainties.

Straightforward approaches such as Monte-Carlo simulations simulations are computationally too expensive. More sophisticated approaches, for example the generalized Polynomial Chaos approach, allow faster convergence and hence less computational effort. However, they are affected by the curse of dimensionality.

The research focuses on the modeling of uncertainties in the context of partial differential equations and efficient methods for the quantification.

References

Georg, Niklas ; Ackermann, Wolfgang ; Corno, Jacopo ; Schöps, Sebastian (2019):
Uncertainty Quantification for Maxwell's Eigenproblem based on Isogeometric Analysis and Mode Tracking.
In: Computer Methods in Applied Mechanics and Engineering, Elsevier, S. 228-244, 350, ISSN 0045-7825,
DOI: 10.1016/j.cma.2019.03.002,
[Online-Edition: https://doi.org/10.1016/j.cma.2019.03.002],
[Article]

Galetzka, Armin ; Bontinck, Zeger ; Römer, Ulrich ; Schöps, Sebastian (2019):
A multilevel Monte Carlo method for high-dimensional uncertainty quantification of low-frequency electromagnetic devices.
In: IEEE Transactions on Magnetics, IEEE, ISSN 0018-9464,
DOI: 10.1109/TMAG.2019.2911053,
[Online-Edition: https://doi.org/10.1109/TMAG.2019.2911053],
[Article]

Ion, Ion Gabriel ; Bontinck, Zeger ; Loukrezis, Dimitrios ; Römer, Ulrich ; Lass, Oliver ; Ulbrich, Stefan ; Schöps, Sebastian ; De Gersem, Herbert (2018):
Robust Shape Optimization of Electric Devices Based on Deterministic Optimization Methods and Finite Element Analysis With Affine Decomposition and Design Elements.
In: Electrical Engineering (Archiv für Elektrotechnik), ISSN 1432-0487,
DOI: 10.1007/s00202-018-0716-6,
[Online-Edition: https://doi.org/10.1007/s00202-018-0716-6],
[Article]

Römer, Ulrich ; Schmidt, Christian ; van Rienen, Ursula ; Schöps, Sebastian (2017):
Low-Dimensional Stochastic Modeling of the Electrical Properties of Biological Tissues.
In: IEEE Transactions on Magnetics, S. 1-4, 53, (6), ISSN 0018-9464,
DOI: 10.1109/TMAG.2017.2668841,
[Online-Edition: https://doi.org/10.1109/TMAG.2017.2668841],
[Article]

Jankoski, Radoslav ; Römer, Ulrich ; Schöps, Sebastian (2017):
Modeling of Spatial Uncertainties in the Magnetic Reluctivity.
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, S. 1151-1167, 36, (4), ISSN 0332-1649,
[Online-Edition: https://doi.org/10.1108/COMPEL-10-2016-0438],
[Article]

Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2016):
Stochastic Modeling and Regularity of the Nonlinear Elliptic curl-curl Equation.
In: SIAM/ASA Journal on Uncertainty Quantification, SIAM, S. 952-979, 4, (1), ISSN 2166-2525,
[Online-Edition: http://dx.doi.org/10.1137/15M1026535],
[Article]

Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2014):
Approximation of Moments for the Nonlinear Eddy Current Model with Material Uncertainties.
In: IEEE Transactions on Magnetics, 50, (2), [Online-Edition: http://dx.doi.org/10.1109/TMAG.2013.2284637],
[Article]

Bartel, Andreas ; De Gersem, Herbert ; Hülsmann, Timo ; Römer, Ulrich ; Schöps, Sebastian ; Weiland, Thomas (2013):
Quantification of Uncertainty in the Field Quality of Magnets Originating from Material Measurements.
In: IEEE Transactions on Magnetics, S. 2367-2370, 49, (5), [Online-Edition: http://dx.doi.org/10.1109/TMAG.2013.2241041],
[Article]

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